Last week I introduced Championship Leverage Index, an index for measuring the impact of a game on a team's World Series title chances. This week I expand on the idea, and introduce Champ LI's sister stat, Championship Win Probability Added.

To review, Champ LI, similar to Tango's Leverage Index, measures the importance of a game relative to an average, neutral game. Last week I showed off the potential of Champ LI by showing graphs of each NL team's Champ LI as the season progressed. Last week's graphs, while informative, lacked one key component - they did not take into account the opponent of the game. It was nice to see the smooth graphs, taking into account only the standings without any odd spikes due to opposition, but to really measure a game's impact, the team's opponent must be considered.

Contrary to what some players and managers may say, all games don't count the same. A Red Sox-Yankees game isn't "just another game", as much as players may try to frame it that way. When a team plays a division rival also contending for the crown, the game takes on added impact - the team not only gets a needed win, but deals a loss to a competitor. So just how much additional impact does playing a division foe bring?

Let's look at a couple of graphs of last season's races to find out. Below is a graph of the Arizona Diamondbacks' Leverage Index over the course of the season. The red bars indicate games against Los Angeles, the D'Backs main rival for the 2008 season.

As you can see, games against LA have an enormous impact compared with games against other teams around the league. However, it varies greatly depending on the time of year. Early season games against LA were not particularly important - only as important as games against other division rivals, which were in turn, only slightly more important than games against non-division rivals. In April, it wasn't yet clear who Arizona would have to compete with for a playoff spot, so the LA games had relatively little additional impact on Arizona's Champ LI. However, by the next time LA rolled into town, it was after the All-Star break and Arizona was up by 1 game on LA and up 7 on the next closest rival. They were also 6 games out of the wild card, so it was becoming clear that LA was the team to beat. Accordingly, their Champ LI skyrocketed from 1.5 to 2.5 for the first game of the Dodgers series. This was cemented even further by the time of their late August and September series, when the Champ LI was nearly doubled for the Dodger games.

Another example, Philadelphia, can be seen below. Games against the Mets and the Brewers are highlighted in red and green respectively.

Again, early in the season, games against New York had little additional impact and games against Milwaukee had no additional impact. However, when it looked like a two team race between Philly and New York in late August, the Phillies' Champ LI dramatically spiked during the New York series. The same happened when Philadelphia dramatically swept Milwaukee in four games in September to get back in the race.

The moral of the story is that, yes, games against rivals contending for the crown really are big games - counting for as much as double the importance of games against non-contending teams. In fact, as it becomes increasingly clear that it is strictly a two-team race, the Champ LI gets closer and closer to doubling when playing the other team in the race.

As a point of curiosity, I'll present this chart of each team's "biggest" games of the year. Most of the games are indeed against a division rival, and were usually the game where everything started to go downhill (for the non-playoff teams) or where the team really took off (in the case of playoff teams). For some, that game came very early in the season (opening day for the Giants), and for others it came late (astute readers will notice slight differences in Champ LI from last week's post. Last week the baseline of the index was an opening day game against a team not contending for the playoffs - however when the possibility of playing a pennant race opponent was factored in, this average used as a baseline increased slightly, making the Champ LI numbers you see here slightly smaller than last week.) Of course, it comes as no surprise that the most important regular season game of the year was the 1-game playoff between the White Sox and Twins.

Now that we finally have the effect of playing division rivals well-understood, I'll explain Championship Win Probability Added. As you've probably already guessed, Champ WPA is analogous to regular WPA, except that instead of measuring how many games a particular play or player won (or lost), it measures how many championships a particular play or player contributed.

The formula for this is very simple. Having already calculated the impact of a win on a team's chance to win the championship, we can simply multiply this number by a particular player's individual WPA to get Champ WPA. Taking account of the impact of both the game and the play within the game, we get the number of championships won. Intuitively, a player who had an individual game WPA of 1.0 (or 100%) during the 7th game of the World Series, would have contributed exactly one world championship to his team.

Let's look at an example in the case of C.C. Sabathia - a player who many consider to have practically carried Milwaukee on his back on the way to the playoffs. Below is a chart of his game by game results with the Brewers and we can see just how much of a World Series championship he earned.

As everyone knows, Sabathia was dominant in his stint with the Brewers - he was 11-2 with a 1.65 ERA. What's interesting is to see that he won about 6% of a World Series title due to his work during the regular season - the biggest game of course being his masterpiece against the Cubs on the final day of the season. However, in his one playoff appearance, he choked away much of his value when he was pounded for 5 runs in 3 2/3 innings - on that single day alone, he gave back 3.5% of a championship, leaving him with a net value of 2.33% of a World Series title with the Brewers. This may not sound like a lot for a player who played so well down the stretch in big games, but the way MLB is set up, the playoffs are what really matter, and it's difficult to make huge impacts without your team going deep into the postseason.

Let's take a look at another guy who was lauded for his big game performance after coming to a new team: Manny Ramirez. I won't print the whole chart here, but Ramirez earned 4.4% of a World Series title during the regular season with the Dodgers, with his most valuable performance coming in a September 7th game against Arizona (Champ WPA of 0.7%), the team's most important game of the year. It took Manny two months of MVP-caliber play in a pennant race to earn 4.4% of a championship, but in the postseason Ramirez bettered it in only 8 games (his most valuable game coming in Game 3 of the NLCS), racking up 7.3% of a World Series title for a total championship contribution of 11.7% with Los Angeles.

It's important to note that I'm not billing Champ WPA as the end all or be all of MVP-stats. Champ WPA does in fact give you the percentage of a championship won by a player, but of course, that is not necessarily the criteria that I would recommend using for the MVP. Champ WPA of course, is also not predictive, and thus is not very useful in player evaluation, but it does measure the actual impact that a player did have in terms of championships. I think that's a fairly noteworthy thing to keep track of, if just from a historical perspective. Francisco Cabrera, in one swing, contributed greater share of a championship (37%) than thousands of better players did in their entire careers. It doesn't mean he was better, it just means he really did contribute more - even if only by luck.

With that disclaimer, I'll wrap up with some fun stuff. Last week I left you hanging in the most important at-bat of the year - the 8th inning of the 7th game of the ALCS - when JD Drew struck out against David Price. How much of a championship did Drew lose with that at-bat? With a WPA of -13% and the game itself worth half of a championship, he lost 6.5% of a World Series title!

However, while that was the at-bat with the largest leverage, that wasn't the biggest championship changing event of 2008. What was? In Game 3 of the World Series, Grant Balfour came on in the bottom of the 9th with no outs and a man on first in a tie game. One pitch later, a wild pitch and a throwing error by Dioner Navarro put the winning run on third. Net result: 8.25% of a World Series title lost.

In the regular season, the biggest play of the year belonged to Ryan Braun's 2-out 8th inning home run giving the Brewers the lead against the Cubs on the last day of the season. The game was meaningless to the Cubs, but to Braun and the Brewers the play earned 2.4% of a World Series title.

Like WPA, Championship Win Probability Added doesn't tell you everything, but it does paint an informed picture of how plays and players impacted a team's chances for a championship over the course of a game, a season, and a career. While you may not want to choose your MVP by it, it's a fun an informative stat in its own right.

Comments

Good stuff, Sky. If I understand correctly, your system calculates ChampLI as the difference between current Champ% and Champ% if the team wins. Now, you are including the impact of the opponent's Champ%, too, if they lose?

Posted by: studes at April 5, 2009 6:01 AM

The system calculates the probability of a team winning the World Series to get its baseline. Then it assumes that the team in question wins it's next game. And the algorithm knows who that next game is against. So now the updated standings will show 1 more win for the team in question and 1 more loss for its opponent. Then it recalculates the probability of the team in question winning the World Series based on the new standings after that one game has been played. The difference between the two probabilities is what creates Champ LI.

Posted by: Sky Andrecheck at April 5, 2009 6:54 AM

I'm fascinated by the logic that says Mark Teixiera was the reason the Angels won so many games despite the fact that they were already 26 games over 500 when they acquired him. Does that make sense to anyone else?

Posted by: Richard at April 5, 2009 7:26 AM

I really like the addition of opponent in the algorithm. It is interesting to see that Arizona's games against LA in mid-July have higher leverage than any non-LA game they play the whole year. It argues for teams in tight races, even early in the season, stacking their rotations, if they can, going into series with division rivals.

Posted by: Dave at April 5, 2009 8:33 AM

The Angels certainly didn't need Tex for the regular season. When they got him the Angels had a Champ LI of .16 and within a couple weeks the Angels games were meaningless. Teixiera's regular season Champ WPA with the Angels: 0.04%.

Posted by: Sky Andrecheck at April 5, 2009 8:35 AM

Sky, any chance you could show a list of last year's top 10 in championships added? It would be nice to see the regular season leaders (to compare with the MVP awards) and the overall leaders including the postseason.

Posted by: Dackle at April 5, 2009 10:21 AM

Is the system closed? How many "Championships Added" are there throughout the 2008 season if you add every player's Champ WPA together? Or is it zero-sum with the pitcher earning negative CWPA for giving up events to the hitter?

Posted by: Ben at April 6, 2009 9:35 AM

Great question Ben. For playoff series, Champ WPA is a zero-sum system, just like regular WPA. So when JD Drew lost 6.5% of a World Series title, David Price won 6.5% of a World Series.

However, things can vary with the regular season. For instance, Braun's homer on the last day of the season gained 2.4% of a World Series title, but for Bobby Howry, who gave up the homer, the game was meaningless, so 0% was lost. By the same token, had the Brewers lost the game, they would have lost 6.25% of a title, while the Cubs would have gained 0% by winning.

So to answer your question, if teams in pennant races BEAT those playing meaningless games, the total Champ WPA will be slightly larger than 1, but if the teams in the pennant races LOSE those games, the total Champ WPA will be slightly smaller than 1.

Posted by: Sky Andrecheck at April 7, 2009 8:19 AM

I'm still unclear how this differs from Studes' system in the HardballTimes.com articles. Sure, there are subtle differences, but isn't the big picture the same?